Structural optimisation with tapered sections

The optimisation principle

In a rigid portal frame the bending moment varies strongly along each member: high at the knee and ridge, lower in between, and near zero at a pinned base. A hot-rolled section has the same depth everywhere and is therefore oversized for most of its length. A tapered built-up member, welded from three plates, can vary web depth, web thickness and flange size along its length to follow the moment diagram. This is the core idea of the pre-engineered building: material is placed only where it is needed. Combined with high-strength steel (typically 345–355 MPa yield) and thin webs, tapered frames commonly use substantially less steel than equivalent frames in uniform hot-rolled sections, though the saving depends on span, loads and serviceability limits.

What gets optimised

Design checks for tapered members

Tapered, slender members require checks beyond those for compact hot-rolled sections:

• Local buckling and slender webs: AISC 360-22 (with AISC Design Guide 25 for web-tapered members), AS 4100:2020, CSA S16-19 and EN 1993-1-5 provide rules for slender plate elements and shear buckling, including tension field action where permitted.
• Lateral-torsional buckling: of the unbraced inner flange in negative moment regions near knees, governed by flange brace spacing.
• Stability analysis: second-order (P-Δ) effects using the direct analysis method (AISC 360-22) or equivalent amplification in AS 4100 and EN 1993-1-1.
• Web-to-flange welds: sized for shear flow; one-sided fillets are common where design and code permit.
• Serviceability: lighter frames are more flexible – see serviceability and deflection limits.

AISC Design Guide 25 (Frame Design Using Nonprismatic Members) and the MBMA Metal Building Systems Manual are key references for US practice.

Building parameters that drive steel weight

Member-level optimisation only works within the geometry the owner chooses. The largest savings are usually made earlier, when the building parameters are set:

Because these choices interact, World Steel's estimators usually price two or three alternatives – for example clear span versus one interior column, or 7.5 m versus 9 m bays – before the design criteria are frozen. The relevant systems are described in clear-span and multi-span buildings.

Limits of optimisation

Optimising for weight alone can increase cost. Very thin webs need more stiffeners and careful handling; many plate thickness changes raise fabrication and welding effort; very slender frames may fail drift limits or vibrate. A good PEB design balances steel weight, fabrication labour, transport (member lengths and container fit), erection simplicity and foundation cost. Optimisation of purlins and girts – lapped Z sections, gauge changes by zone – adds further savings in secondary framing.

How WSC applies optimisation

World Steel designs frames with dedicated PEB software and its in-house engineers, then fabricates the tapered members on automatic welding lines (see automatic welding of built-up members). Designs follow the client's code and serviceability criteria; optimisation is never allowed to override code checks. Typical steps are: agree design criteria and serviceability limits; run a first analysis with standard member depths; iterate web depth, plate thicknesses and splice positions; position flange braces to suit the purlin and girt layout; and finally rationalise plate sizes so that the shop can nest web plates efficiently from standard plate widths and minimise the number of different thicknesses ordered. The result is a frame that is light, but also simple to cut, weld, ship and erect. This is part of WSC's design service for pre-engineered buildings.